This paper investigates the ultra reliable and low latency communication (URLLC) performance of the IRS-aided MIMO system. The upper and lower bounds of the optimal average error probability (OAEP) for the coding rate within 1/sqrt(Mn) of the capacity are derived, where n and M represent the blocklength and the number of transmit antennas, respectively. To achieve this goal, a new central limit theorem (CLT) for the mutual information density over the IRS-aided MIMO system is derived in the asymptotic regime where the block-length, the IRS size, and number of the antennas go to infinity with the same pace. The CLT is then utilized to derive the closed-form upper and lower bounds for the OAEP. Based on the analysis result, a gradient-based algorithm is proposed to minimize the lower bound of the OAEP by optimizing the phase shift of the IRS. Simulation results validate the fitness of the CLT and the effectiveness of the proposed algorithm in optimizing the theoretical bound, as well as the performance of practical LDPC code.

翻译：本文研究了IRS辅助MIMO系统的超可靠低延迟通信(URLLC)性能。推导了编码速率在容量1/√(Mn)范围内的最优平均错误概率(OAEP)的上界和下界，其中n和M分别代表块长和发射天线数量。为实现该目标，在块长、IRS尺寸及天线数量以相同比例趋于无穷大的渐近条件下，推导了IRS辅助MIMO系统互信息密度的新中心极限定理(CLT)。利用该CLT进一步得到了OAEP的闭式上界和下界。基于分析结果，提出了一种梯度算法，通过优化IRS的相位偏移来最小化OAEP下界。仿真结果验证了CLT的适用性，以及所提算法在优化理论界和实际LDPC码性能方面的有效性。